One of the features that makes Mathematica and Matlab so useful is their built-in 3D plotting for multivariable surfaces and objects. Matplotlib does this very easily in Python, but the features are so rich we can only touch on a few of them here. For more, take a look at the other examples on the [http://matplotlib.org/examples/index.html examples on the matplotlib website].

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One of the features that makes Mathematica and Matlab so useful is their built-in 3D plotting for multivariable surfaces and objects. Matplotlib does this very easily in Python, but the features are so rich we can only touch on a few of them here.

As an appetizer, consider surface3d_demo2.py from matplotlib:

As an appetizer, consider surface3d_demo2.py from matplotlib:

Revision as of 05:56, 19 February 2013

The Python matplotlib module adds tools for interactive 2-D and 3-D graphics to our very short course in Python for scientific research. Matplotlib provides for easily generating and saving plots in file formats you can display on the web or in other programs, print, and incorporate in documents.

Installation of matplotlib

The current version 1.2 may be included in some Linux distributions. Version 1.1 has most of the features you will need now, and it is in Ubuntu and OpenSuse packages that can be added to your core Python system after you also install numpy. For example, under Ubuntu you would use

sudo apt-get install python-matplotlib

to get the most recent version available for your system and resolve missing components.

Once you have it installed, programs that use this library will have to import it with lines such as

import numpy as np
import matplotlib as plt

to make the functions available. With these, numpy functions will start with np. and mathplotlib functions will have plt. in front of the function name, which shortens the code you would write. You can check that your computer has numpy and matplotlib by trying these commands in interactive Python or Idle. The version numbers will be available too with

Most of this program is used to create and prepare the data lists. The plotting is done in one line! We add labels to axes, a title to the plot, and show the work. The way in which it appears will depend on our installation, but the default is a Tkl interface that offers control for panning, zooming, and saving as png file. The data go into the plot as lists, and appear by default as a drawn line connecting the points. However, if you prefer red circles to a "pen down" line, then change the plt.plot to

plt.plot(time,amplitude,'ro')

or to

'r--' # red dashes
'bs' # blue stars
'g^' # green triangles

The properties of the line would be controlled by variables in the plot function using MATLAB-style string/value pairs.

Saving the plot to a file

The savefig function is sensitive to the file type in the extension, and

fname = 'oscillator.ps'
plt.savefig(fname,dpi=600)

would be an example of a PostScript figure set to 600 dots per inch resolution. Supported formats are intended for high quality reproduction and include eps, ps, pdf, png, and svg, among others. The resolution may be controlled within the program, or in defaults for the user's custom startup file.

Overplotting and separated plots

Matplotlib's pyplot.plot takes two arrays as arguments and is aware of several modifiers that determine how the data are plotted. When you use plot, you should be aware that implicitly it creates
a figure and a subplot, and then uses these with the data you have provided. The subplot(nrows, ncols, plot_number) function allows you to make arrays of 9 or fewer plots on the same page. When you only have one plot, it is subplot(1,1,1). You are allowed to leave out the commas if the result is unambiguous, and you will sometimes see this written (lazily) as subplot(111). A second subplot on row 2 would be subplot(212) and so on.

If the pyplot.plot function is repeated, it loads another set of x-y data into the one plot, each set with its own properties. The sets can be labeled, and the labels can be turned into legends in the plot. Here's a simple example:

Tick marks and data ranges

You've noticed that when data are loaded as a list or tuple, the plot function automatically selects the data range for both axes, and supplies tick marks. You may add minor ticks and control their properties
with

With these limits, the range of x shown will be from -10 to +10 instead of the range in the x-data, and y will be shown from -200 to +200.

A little 3D plotting

One of the features that makes Mathematica and Matlab so useful is their built-in 3D plotting for multivariable surfaces and objects. Matplotlib does this very easily in Python, but the features are so rich we can only touch on a few of them here.

The first line imports a toolkit that provides 3d projection. For this one, you would need the mpl_tookits package.

The second line imports matplotlib.pyplot and uses plt to stand for it in our code.

The third line imports numpy, numerical Python, which we are going to look at in more detail later. Here, it provides a way to handle the data transparently even if you do not know how the code works yet.

We create a figure called "fig", and we add one and only one subplot "ax" that will hold our work. Notice that the subplot is a "3d" projection.

Numpy is used to create two linear arrays, one from 0 to 2 Pi that we think of as Phi, the azimuth angle in spherical coordinates. The other, from 0 to Pi, is Theta, the altitude of spherical coordinates. From these we calculate a set of x, y, and z that are the coordinates of points on a surface. Here, "np.outer" means "outer product" of two linear arrays, that is each of x, y, and z are matrices that contain the coordinates (x,y,z) of points on the unit sphere or radius 10 selected by the angles u and v.

The plotting is done in one line from the mpl toolkit with plot_surface(), and then dislayed for us to use with show().

From that little program we get an interactive 3D display of a sphere that looks like this: